2.1 Derivatives and Rates of Change

2.1 Derivatives and Rates of Change - The derivative is...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Derivatives and Rates of Change Section 2.1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Average Rate of Change l The average rate of change of a quantity over a period of time is the amount of change divided by the time it takes. l The average rate of change over the interval [a, b] = ( ) ( ) f b f a b a - -
Background image of page 2
Slope of Secant Line (c, f(c)) (c + ,f(c + ) x x ) ( ) ( c f x c f - + x x x c f x c f m - + = ) ( ) ( sec
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Average Rate of Change
Background image of page 4
Slope of a Tangent Line: derivative of f at a number a l The slope of the curve y=f(x) at the point P(a, f(a)) is the number provided the limit exists.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The derivative is also considered the instantaneous rate of change. ( ) ( ) '( ) lim +-= = h f a h f a f a m h Slope of a Tangent Line (derivative) at a point P (a, f(a)) Normal to a Curve l The normal line to a curve at a point is the line perpendicular to the tangent at that point. Joke Time l What did pi say to i? l Get real! l What did i say to pi? l Be rational! l What did one-half say to one? l Youre so full of yourself!...
View Full Document

Page1 / 10

2.1 Derivatives and Rates of Change - The derivative is...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online